Despite the many successful applications of deep learning models for multidimensional signal and image processing, most traditional neural networks process data represented by (multidimensional) arrays of real numbers. The intercorrelation between feature channels is usually expected to be learned from the training data, requiring numerous parameters and careful training. In contrast, vector-valued neural networks (referred to as V-nets ) are conceived to process arrays of vectors and naturally consider the intercorrelation between feature channels. Consequently, they usually have fewer parameters and often undergo more robust training than traditional neural networks. This article aims to present a broad framework for V-nets. In this context, hypercomplex-valued neural networks are regarded as vector-valued models with additional algebraic properties. Furthermore, this article explains the relationship between vector-valued and traditional neural networks. To be precise, a V-net can be obtained by placing restrictions on a real-valued model to consider the intercorrelation between feature channels. Finally, I show how V-nets, including hypercomplex-valued neural networks, can be implemented in current deep learning libraries as real-valued networks.

中文翻译：

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了解向量值神经网络及其与实数和超复值神经网络的关系：将特征之间的互相关性纳入神经网络[超复杂信号和图像处理]


尽管深度学习模型在多维信号和图像处理方面有许多成功的应用，但大多数传统神经网络处理由（多维）实数数组表示的数据。特征通道之间的相互关联通常需要从训练数据中学习，需要大量的参数和仔细的训练。相比之下，向量值神经网络（称为 V 网）被设计为处理向量数组并自然地考虑特征通道之间的相互相关性。因此，与传统神经网络相比，它们通常具有更少的参数，并且通常经过更稳健的训练。本文旨在提出 V 网的广泛框架。在这种情况下，超复值神经网络被视为具有附加代数属性的向量值模型。此外，本文还解释了向量值神经网络和传统神经网络之间的关系。准确地说，可以通过对实值模型进行限制来考虑特征通道之间的互相关性来获得V网。最后，我展示了如何在当前的深度学习库中将 V 网络（包括超复值神经网络）实现为实值网络。